Greatest Common Factor of 1974 and 1981
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 1974, 1981 i.e. 7 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 1974 and 1981 is 7.
GCF(1974,1981) = 7
GCF of 1974 and 1981
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 1974 and 1981 by prime factorization method
- Greatest Common Factor of 1974 and 1981 by matching factors method
GCF of 1974 and 1981 is 7
Prime Factorization of 1974
| 2 | 1974 |
| 3 | 987 |
| 7 | 329 |
| 47 | 47 |
| 1 |
Prime factors of 1974 are 2,3,7,47. Prime factorization of 1974 in exponential form is:
1974 = 21×31×71×471
Prime Factorization of 1981
| 7 | 1981 |
| 283 | 283 |
| 1 |
Prime factors of 1981 are 7,283. Prime factorization of 1981 in exponential form is:
1981 = 71×2831
∴ So by taking common prime factors GCF of 1974 and 1981 is 7
Greatest Common Factor of 1974 and 1981 by matching factors method
Factors of 1974
List of positive integer factors of 1974 that divides 1974 without a remainder.
1,2,3,6,7,14,21,42,47,94,141,282,329,658,987,1974
Factors of 1981
List of positive integer factors of 1981 that divides 1981 without a remainder.
1,7,283,1981
Greatest Common Factor
We found the factors and prime factorization of 1974 and 1981. The biggest common factor number is the GCF number.
So the greatest common factor 1974 and 1981 is 7.
Also check out the Least Common Multiple of 1974 and 1981
Properties of GCF 1974 and 1981
(i) The GCF of 1974 and 1981 is associative
GCF of 1974 and 1981 = GCF of 1981 and 1974
Related Greatest Common Factor of 1974
Related Greatest Common Factor of 1981
Frequently Asked Questions on GCF of 1974 and 1981
1. What is the GCF of 1974 and 1981?
Answer: GCF of 1974 and 1981 is 7.
2. What are the Factors of 1974?
Answer: Factors of 1974 are 1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974. There are 16 integers that are factors of 1974. The greatest factor of 1974 is 1974.
3. What are the Factors of 1981?
Answer: Factors of 1981 are 1, 7, 283, 1981. There are 4 integers that are factors of 1981. The greatest factor of 1981 is 1981.
4. How to Find the GCF of 1974 and 1981?
Answer:
Greatest Common Factor of 1974 and 1981 = 7
Step 1: Find the prime factorization of 1974
1974 = 2 x 3 x 7 x 47
Step 2: Find the prime factorization of 1981
1981 = 7 x 283
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 7
Step 4: Therefore, the greatest common factor of 1974 and 1981 is 7